DFS acdrean 1431

C - Sum vs Product

Time Limit:1000MS     Memory Limit:64000KB     64bit IO Format:%lld & %llu

Submit Status Practice ACdream 1431

Appoint description: 
System Crawler  (2015-04-16)

Description

Peter has just learned mathematics. He learned how to add, and how to multiply. The fact that 2 + 2 = 2 × 2 has amazed him greatly. Now he wants find more such examples. Peters calls a collection of numbers beautiful if the product of the numbers in it is equal to their sum.

For example, the collections {2, 2}, {5}, {1, 2, 3} are beautiful, but {2, 3} is not.

Given n, Peter wants to find the number of beautiful collections with n numbers. Help him!

Input

The first line of the input file contains n (2 ≤ n ≤ 500)

Output

Output one number — the number of the beautiful collections with n numbers.

Sample Input

2
5

Sample Output

1
3

Hint

The collections in the last example are: {1, 1, 1, 2, 5}, {1, 1, 1, 3, 3} and {1, 1, 2, 2, 2}.

#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<cstdlib>
#include<algorithm>
#include<queue>
#include<vector>
#include<stack>
using namespace std;
int n,ans;
void dfs(int x,int k,int product,int sum)
{
    for(int i=x;i>=2;i--)
    {
        if(product*i>sum+i+n-k) continue;
        else if(product*i==sum+i+n-k) ans++;
        else dfs(i,k+1,product*i,sum+i);
    }
}
int main()
{
    scanf("%d",&n);
    dfs(n,1,1,0);
    printf("%d\n",ans);
    return 0;
}